Here is the paragraph:
>If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations: (i) Spacetime is a **pseudo-Riemannian manifold** *M*, endowed with a **metric tensor** and governed by geometrical laws. (ii) Over *M* is a **vector bundle** *X* with a **non-abelian gauge group** *G*. (iii) **Fermions** are sections of **(Ŝ +⊗VR)⊕(Ŝ ⊗VR¯)(Ŝ+⊗VR)⊕(Ŝ⊗VR¯)**. ***R*** and ***R*****¯** are not **isomorphic**; their failure to be **isomorphic** explains why the light fermions are light and presumably has its origins in representation difference Δ in some underlying theory. All of this must be supplemented with the understanding that the geometrical laws obeyed by the **metric tensor**, the **gauge fields**, and the **fermions** are to be interpreted in quantum mechanical terms.
>
>Edward Witten, “Physics and Geometry”
According to Eric Weinstein (who I know is a controversial figure, but let’s leave that aside for now), this is the most beautiful and important paragraph written in the English language. You can watch him talk about it [here](https://youtu.be/vdW9XDBuxjU?t=3079) or take a deep dive into his [Wiki](https://theportal.wiki/wiki/Graph,_Wall,_Tome).
Could someone (1) literally translate the paragraph so a layman can grasp the gist of it, switching the specific jargon **in bold** with simplified plain English translations? Just assume I have no formal education in math or physics, so feel free to edit the flow of the paragraph for clarity’s sake. For example, something like:
>If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations: (i) Spacetime is a ~~pseudo-Riemannian manifold~~ ***flexible*** ***3-dimension space*** *M*, endowed with a ~~metric tensor~~ **composite list of contingent quantities** and governed by geometrical laws… etc.
And (2) briefly explain the importance of this paragraph in the big picture of physics?
In: Physics
1) Space is flexible with time, in a specific squishy way. Call it “M” because we’ll refer to it later. The squishiness of space and time follows a specific set of rules for 3D manipuation, called a “pseudo-Riemannian manifold”. The way it squishes is called a tensor, and it follows geometrical laws. There are a bunch of formulas involved in that manipulation, but it means you can convert between time and space, that stuff in space affects time, and stuff in time affects space.
2) There are a bunch of values well call “X” that can modify space and time. They represent forces and fields. They follow special ordering rules, and form a gauge group. You can use these values X to modify the squishy thing in the first point. These things represent energy and motion. They have specific ordering requirements, and they cannot be easily reversed. As an ELI5 of that if you have 3 and you subtract 3 you don’t always get 0; if you want to get zero again you have to do extra steps. These explain the relationship of how you can squish space and time around to change their shapes.
3) Subatomic particles that make up matter, called fermions, that all meet a general pattern. This things make up mass. The pattern formula has multiple solutions, and includes both a positive side and negative side. Even though it has two sides, they’re not opposites from each other like you would have +3 and -3 that are equal and map to each other, the two opposite sides are not isomorphic. These things still have some big questions to be answered, but they explain how you can manipulate matter and space. (There is another set, called bozons, that have a similar relationship with energy).
So an ELI5 rewrite:
> We can see three fundamental things about the universe: (1) Space and time are squishy according to a set of rules. We have math that predicts it. (2) Squishing space and time depends on ordering and a second set of rules, and any squishes generally cannot be easily undone. We have math for predicting this, too. (3) Subatomic particles another set of rules that build all matter, but we only have most of the math to model it, not quite all of it for a complete model.
> Putting those three topics together gives all our current rules for space, time, energy, motion, and mass, and conversions between them.
Using those general words describes the relationship of all the various conversions and systems we know in physics. The next picture in the video shows a clip of a wall that depicts a bunch of the relationships. Some are well known, like how E=mc^2 is the relationship between energy and matter and explains things like why converting matter into energy in an atomic bomb creates huge amounts of energy. Others explain relationships with space and distance, and relationships with time. They all inter-relate, something that relates with space and distance and time also must relate with motion and force.
I don’t think it’s particularly beautiful, but I can see why he likes it as a short summary of our current physics models.
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